Undiversifying during Crises: Is It a Good Idea?

Abstract

High levels of correlation among fi nancial assets, as well as extreme losses, are typical during crisis periods. In such situations, quantitative asset allocation models are often not robust enough to deal with estimation errors and lead to identifying underperforming investment strategies. It is an open question if in such periods, it would be better to hold diversifi ed portfolios, such as the equally weighted, rather than investing in few selected assets. In this paper, we show that alternative strategies developed by constraining the level of diversifi cation of the portfolio, by means of a regularization constraint on the sparse l q -norm of portfolio weights, can better deal with the trade-off between risk diversifi cation and estimation error. In fact, the proposed approach automatically selects portfolios with a small number of active weights and low risk exposure. Insights on the diversifi cation relationships between the classical minimum variance portfolio, risk budgeting strategies, and diversifi cation-constrained portfolios are also provided. Finally, we show empirically that the diversifi cation-constrainedbased l q -strategy outperforms state-of-art methods during crises, with remarkable out-of-sample performance in risk minimization.